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This article mainly studies the time-varying fixed-time formation (FTF) tracking control problem for stochastically disturbed nonlinear multi-agent systems on detail balanced graphs. First, a novel sufficient condition for ensuring the fixed-time stability in probability of stochastic differential equation is given. Then, using the neighboring information, a simple discontinuous control protocol is designed for achieving time-varying FTF. By means of non-smooth analysis techniques, our control objective is obtained and a proper upper bound for the expectation of the stochastic settling time is estimated. Finally, a numerical illustration demonstrates that the proposed control protocol is effective.

The multi-agent-based supply chain network is a dynamic system consisting of multiple subchains connected by information flows, material flows and capital flow, etc. The consensus of multi-agent systems is often applied to the cooperation between subchains and inventory management in supply chain networks. Considering the ubiquitous external disturbances, this paper mainly considers the fixed-time consensus of a stochastic three-echelon multi-agent-based supply chain system. A nonlinear feedback fixed-time control protocol is constructed for ensuring the consensus of the considered supply chain network. Using the stability theory of stochastic differential equations, sufficient conditions for the fixed-time consensus and the upper bound estimation of the settling time are obtained. Finally, the validity of the control protocol and the correctness of the theoretical analysis are revealed by numerical simulation.

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